This is my personal perspective on why i would wanna get a compact instead of a DSLR,
but of course i will try to stand from a middleman's perspective to write this.
I will touch on few reasons why people want a compact and facts about a compact.
1) The price
Firstly, let's ask ourselves, are compacts THAT cheap?
A brand new canon ixus 110 is costs $569 with freebies,
if we minus the freebies, it would probably cost around $500 flat.
With that amount of money, i could get a D40 with the kit lens (18-55mm II),
and another manual focus lens to compliment it, along with a decent SD card with good write-speed.
So why get a compact still?
Because compacts are a very confined range of products, they don't have much to complement it.
Sans tripod, memory cards, cases, there really isn't much to buy for a compact.
Unless we're talking about a new camera, that is.
Money matters:
1) People who are just starting to venture into photography may want to get a compact to start first, in case they're not sure whether they want to continue venturing into photography before investing in a DSLR.
2) People who don't have the budget
3) Some have the budget, yet don't want to buy a DSLR but instead just a good compact camera.
2) Size
The compact's size is well, rather compact depending on models.
Still, they are relatively small.
Many normal folks who are not into photography, find it a hassle to bring a DSLR around when going out.
To us who are into photography, find it normal but to them, it's troublesome.
First, you will need a bag to put your SLR, DSLR as you won't want to throw it in a bag with too little paddings.
Secondly, it's not easy to retrieve it if you need to capture and instantaneous moment (unless you're hanging it around your neck).
That's why people settle for compacts.
Many youngsters now buy compact cameras and just slip it into their pockets when going out with friends,
and this is the same for many other people.
Compacts are better for normal people who do not want the size and bulk of the DSLR as all they want is just to take photos.
3) Image Quality
The image quality has nothing to do with how many megapixel a camera has, which is a common mistake.
The megapixels merely tells you how large you can blow up the photo while printing optimumly.
The image quality on a compact is honestly quite good.
They can also produce good shots.
Most compacts have ability to shoot in macro mode,
but mainly fail in creating a shallow depth of field needed to singulate the object which the photographer wises to bring out.
This can happen eve when the compacts are at wide open at f/2.8.
However, when zooming a different story is to be told.
When a lens zooms out, the image quality should remain as good as it were when it was at it's widest.
But understandably, for it's price, when a camera is at 15x, the image quality drops and even the object is barely in focus.
Casio also recently introduced a compact camera that had the ability to shoot up to 30 frames per second.
Many were wowed at this and was a good selling point but the image quality was to be lowered to 6.1 megapixels.
But who cares? No Compact had the ability to do that. That was a breakthrough in compact camera technology.
This was something they want, burst mode, without having to get a DSLR, they could now get it,
at an even faster rate then a DSLR, to be exact, thrice the rate faster then the faster DSLR going at 11FPS (Nikon D3 on DX mode).
4) Convenience
This partially been mentioned in size where people will want a small camera just to capture simple moments,
of their kids and family. They don't want something complicated for artistic photography and are not that into photography.
This appeals to them and they will definitely choose this over the DSLR, SLR or RF.
5) Niche Market
In every market, there will definitely be a niche market.
The compact camera market is no exception.
Niche camera or the top-grade cameras of compact don't come cheap either.
Some people just don't want a DLSR, but instead a good compact that looks sleek and works well.
The LX3 is a "bridge camera between a prosumer and a compact".
With vario-summicron lens from LEICA AG Germany built-in, setting to shoot on raw or jepg shows that a compact can be complicated and good too.
With ISO ranges from 80-3200, you're good to shoot in nearly any conditions, coupled with it's powerful flash however for serious shooting, anything above 400 is not recommended,
but i feel ISO 800 is still ok.
Similar to the LX3, aka the sister of the LX3, the Leica Digilux 4 has been hailed haute couture of the compact camera line.
Nearly identical in function to the LX3, it has the same abilities as mentioned above but of course is more stylish and cost ALOT more then the LX3.
With a hot-shoe on the top of the camera, it allows the camera to mount a flash, external viewfinder.
There are also specialised lens accessories from panasonic for their LX3 such as a neutral density (GND) filter meant sepcially for the LX3.
The leica digilux 4 also offers 3 different aspect ratios, namely 4:3, 3:2 and 12:9.
They even have a AE-L and AF-L button, and one may ask, all these advanced features on a compact?
Well, i won't call this compact. The leica digilux-4 has even it's own line of accessories, cases and even limited edition series,
such as the safari green one which comes with the leica nylon bag, and the titanium version, only 275 pieces worldwide, with the calf leather casing.
These compacts have became a fashion icon, and everyone wants to own one.
6) Conclusion
In conclusion, if you're a DSLR user, no harm getting one right?
If you're new to photography, why not get one to start your photographic journey?